By Dmitry Solovyov

OSH, Kyrgyzstan (Reuters) - Whoever takes over the Central Asian state of Uzbekistan after its president's death faces a challenge to keep a lid on Islamist militants who have become foot soldiers in global jihadist groups.

Uzbek fighters are deeply embedded in Islamic State in Iraq and Syria, fight alongside the Taliban in Afghanistan, have secret outposts in the biggest Russian cities and have ties with Muslim militants from China who reject Beijing's rule.

Veteran Uzbek leader Islam Karimov, who died last week from a stroke, used brutal methods and a vast security apparatus to keep tabs on a militant movement born in the 1990s out of an insurgency in Uzbekistan, a former Soviet republic.

With Karimov dead and a lack of clarity on who will succeed him, despite Prime Minister Shavkat Mirziyoyev being named interim president by parliament, the security forces' ability to contain the Islamist network is unclear.

Uzbek militants have not had as high a profile as other groups in the global jihadi movement. While fighters from Iraq, Tunisia, Russia and western Europe command units and lead suicide attacks, Uzbeks tend to form the rank-and-file.

But Reuters interviews with security officials, militant fighters and their families indicate that the Uzbek fighters number in the thousands, are battle-hardened and skilled at networking with other jihadist groups.

These fighters view the Uzbek authorities as "Taghut", a Koranic term for tyrants who set themselves up as false Gods, and most now focus on waging jihad abroad.

But in a report last year, the International Crisis Group wrote: "Should a significant portion of these radicalized migrants return, they risk challenging security and stability throughout Central Asia."

MILITANTS BRED IN VALLEY

The heart of Islamist militancy in Central Asia is the Ferghana Valley, a fertile and densely populated strip of land that straddles Uzbekistan, Tajikistan and Kyrgyzstan.

Sitting in the yard of his home in Osh, a Kyrgyz city in the Ferghana valley where a large part of the population are ethnic Uzbeks, 57-year-old ethnic Uzbek Abdurasul Yuldashev described how his estranged wife went to Syria with their son and two daughters while he was away working in Russia.

In Syria, the son, 19-year-old Mukhammadislam, joined an Islamist group.

"One day I received a call from an unidentified number and someone said: 'Congratulations, your son has become a shahid'," Yuldashev said, using the Arabic term for a martyr. He said he shouted at them, and they called him a "kafir", or infidel.

Malokhat Mamatadzhiyeva, a 41-year-old ethic Uzbek who lives in Osh, received a similar call on July 9 last year informing her about the death of her son, Nurmukhammad.

She said he had gone to the Russian city of Vladimir to work on a construction site but told her in November 2014 that he was going to a remote location in Russia for work. The next time she heard from him, in March 2015, he was calling from Syria.

"I started weeping. I said: 'Do not leave me.' But the call got cut off," Mamatadzhiyeva said. She later learned that he had been killed in the fighting in Syria.

SYRIA BATTLEFIELD

Ethnic Uzbeks are active in militant groups in Afghanistan and parts of Pakistan, according to a wanted list of militants published by the United Nations.

Security officials say the militants also have ties to militants from the Chinese Uighur ethnic group, who reject Beijing's rule. A suicide bomb attack on China's embassy in Kyrgyzstan last month was ordered by Uighur groups, and several ethnic Uzbeks helped organize it, Kyrgyz state security say.

Ethnic Uzbeks operate in their own fighting units in Syria, according a Russian who fought there.

"There was a decent number of them," said the fighter, who has now left Syria and asked not to be identified.

Last year state security officials in Osh detained several people on allegations they fought alongside militants in Syria.

In a videotaped interrogation shown to Reuters at the time in Osh, one of them said he went to Syria in October 2013 and for three months was a fighter with the Nusra front, then an affiliate of al Qaeda.

The man, an ethnic Uzbek, said he was ordered to return to Central Asia to carry out attacks. Reuters was unable to establish whether he had made his statement under duress.

There is no evidence Uzbek fighters plan to leave Syria and Afghanistan en masse to launch attacks in Uzbekistan. But they could return home if Islamic State is squeezed out of the territory it controls in northern Syria and Iraq. This could be a concern for the government and foreign states.

"Practically everyone overseas will be ready to recognize any form of rule in Uzbekistan that is going to guarantee stability," said Kazakh political analyst Dosym Satpayev.

(Additional reporting by Olzhas Auyezov in Almaty and Maria Tsvetkova in Moscow, Writing by Christian Lowe,; Editing bv Timothy Heritage)